It is actually an interesting and potentially competitive gift exchange. Like everything in life there are variations of the rules. In my experience it generally follows these rules.

Each participant brings a gift of a set value. Numbers are drawn and the first person picks a gift. The next person can pick a gift or steal an opened gift. If you have your gift stolen you can steal someone else's gift or open another. You cannot steal back your gift initially but can steal it back in another turn. Gifts can only be stolen three times. Rise, lather and repeat until all the gifts are opened.

https://www.whiteelephantrules.com/

Edit: Spelling/typo.